The sum is the total when numbers are added together.

The difference is the result of subtracting one number from another. How much one number differs from another.

Explain why there is sometimes only one solution to a problem

Maths

Compare the structure of problems with one or two unknowns

Represent the structure of a problem with two unknowns in context

Represent and solve problems with two unknowns efficiently

Use a bar model to represent spatial problems with two unknowns

Explain how to represent an equation with a bar model

Solve problems with two unknowns in a range of contexts

Explain how you know you have found all the possible solutions to a problem with two unknowns

Explain how to balance an equation with two unknowns

Solve problems with two unknowns with one, several and infinite solutions

In this unit pupils will compare and represent the structure of problems with two unknowns using a bar model. They will systematically solve problems with two unknowns using trial and improvement. In the future unit this understanding is formalised through the use of algebraic notation. 

In the prior unit pupils explained how to balance equations with addition or subtraction expressions and used knowledge of balancing equations to solve problems. In this unit pupils will compare and represent the structure of problems with two unknowns using a bar model. They will systematically solve problems with two unknowns using trial and improvement.

In this unit pupils will compare and represent the structure of problems with two unknowns using a bar model. They will systematically solve problems with two unknowns using trial and improvement.

Solving problems with two unknowns

When the difference and sum of two unknown numbers is known, there are how many possible solutions?

a represents a larger number. b represents a smaller number. The sum of a and b is 60, and the difference between them is 10
What number does a represent?

a represents a larger numbers and b represent a smaller number. 
The sum of a and b is 205, and the difference between them is 25
What number does b represent?

Steven is 24 years younger than his mum. The sum of their ages is 68 years. How old is Steven’s mum? {{ }} years old.

The sum of two numbers is 140
One number is three times the size of the other number. What are the two numbers?

The sum of two numbers is 410
One number is one-quarter times the size of the other number.  What is the value of the largest number?

Calculate the size of a in this representation.

Calculate the size of c in this representation.

Calculate the size of e in this bar model.

Andeep and Izzy are selling 60 ice poles. Izzy sells 8 ice poles more than Andeep. How many ice poles does Izzy sell?

Andeep and Izzy have read 348 pages altogether. Andeep has read 32 more pages than Izzy. How many pages has Andeep read? 

Explain why there is sometimes only one solution to a problem

Lesson outcome